a) Consider the wing of an aircraft as a flat plate of 25 m length in the flow directi (Figure 2). The plane is moving at 100 m/s in air that is at a pressure of 0.7 bar a a temperature of 10°C. The top surface of the wing absorbs solar radiation at a ra of 800 W/m2. Assume the wing to be of solid construction and to have a sing uniform temperature. Estimate the steady-state temperature of the wing. Refer Table A-15 for air thermophysical properties.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Problem 1.1MA
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Q2 a) Consider the wing of an aircraft as a flat plate of 25 m length in the flow direction
(Figure 2). The plane is moving at 100 m/s in air that is at a pressure of 0.7 bar and
a temperature of 10°C. The top surface of the wing absorbs solar radiation at a rate
of 800 W/m2. Assume the wing to be of solid construction and to have a single,
uniform temperature. Estimate the steady-state temperature of the wing.
Refer Table A-15 for air thermophysical properties.
Air
a conv
9's,abs = 800 W/m²
Į
U= 100 km/s
Too=263 K
p= 0.7 bar
a conv
tam
Figure 2
- Ts
L = 2.5m
Transcribed Image Text:Q2 a) Consider the wing of an aircraft as a flat plate of 25 m length in the flow direction (Figure 2). The plane is moving at 100 m/s in air that is at a pressure of 0.7 bar and a temperature of 10°C. The top surface of the wing absorbs solar radiation at a rate of 800 W/m2. Assume the wing to be of solid construction and to have a single, uniform temperature. Estimate the steady-state temperature of the wing. Refer Table A-15 for air thermophysical properties. Air a conv 9's,abs = 800 W/m² Į U= 100 km/s Too=263 K p= 0.7 bar a conv tam Figure 2 - Ts L = 2.5m
TABLE A-15
Properties of air at 1 atm pressure
Dynamic
Kinematic
Prandtl
Temp., Density,
Specific
Heat,
Cp. J/kg. °C
Thermal
Conductivity,
k, W/m. °C
Thermal
Diffusivity,
a, m²/s
Viscosity,
Number,
T, °C
p. kg/m³
Viscosity,
v, m²/s
μ, kg/m-s
Pr
-150
2.866
983
-100 2.038
3.013 x 10-6
5.837 x 10-6
966
0.01171
0.01582
0.01979
0.02057
0.7246
0.7263
0.7440
-50 1.582
-40 1.514
999
9.319 x 10-6
1002
1.008 x 10-5
0.7436
1004
0.02134
-30 1.451
-20 1.394
-10
8.636 x 10-6
1.189 x 10-6
1.474 x 10-5
1.527 x 10-5
1.579 x 10-5
1.630 x 10-5
1.680 x 10-5
1.729 x 10-5
1.754 x 10-5
1.778 x 10-5
1005
0.02211
1.341
1006
0.02288
1.087 x 10-5
1.169 x 10-5
1.252 x 10-5
1.338 x 10-5
1.382 x 10-5
0.7425
0.7408
0.7387
0.7362
1006
0.02364
1006
0.02401
1006
0.02439
1.426 x 10-5
1.470 x 10-5
0.02476
0 1.292
5 1.269
10 1.246
15 1.225
20 1.204
25 1.184
30 1.164
35 1.145
40 1.127
1.802 x 10-5
0.7350
0.7336
0.7323
0.7309
1007
1007
0.02514
1.516 x 10-5
1.825 x 10-5
1.849 x 10-5
1.562 x 10-5
0.02551
0.02588
1.872 x 10-5
1007
1007
1007
1007
0.7296
0.7282
0.7268
0.7255
0.02625
0.02662
0.02699
1.608 x 10-5
1.655 x 10-5
1.702 x 10-5
1.750 x 10-5
1.895 x 10-5
1.918 x 10-5
1.941 x 10-5
45 1.109
1007
50 1.092
1007
0.02735
1.963 x 10-5
1.798 x 10-5
1.896 x 10-5
1.059
1007
60
70 1.028
0.02808
0.7241
0.7228
0.7202
0.7177
2.008 x 10-5
2.052 x 10-5
1007
0.02881
1.995 x 10-5
4.158 x 10-6
8.036 x 10-6
1.252 x 10-5
1.356 x 10-5
1.465 x 10-5
1.578 x 10-5
1.696 x 10-5
1.818 x 10-5
1.880 x 10-5
1.944 x 10-5
2.009 x 10-5
2.074 x 10-5
2.141 x 10-5
2.208 x 10-5
2.277 x 10-5
2.346 x 10-5
2.416 x 10-5
2.487 x 10-5
2.632 x 10-5
2.780 x 10-5
2.931 x 10-5
3.086 x 10-5
3.243 x 10-5
3.565 x 10-5
3.898 x 10-5
4.241 x 10-5
4.593 x 10-5
4.954 x 10-5
5.890 x 10-5
6.871 x 10-5
7.892 x 10-5
8.951 x 10-5
1.004 x 10-4
1.117 x 10-4
1.352 x 10-4
1.598 x 10-4
1.855 x 10-4
2.122 x 10-4
2.398 x 10-4
3.908 x 10-4
80 0.9994
1008
0.02953
2.096 x 10-5
2.097 x 10-5
0.7154
90 0.9718
1008
2.139 x 10-5
2.201 x 10-5
1009
2.181 x 10-5
2.306 x 10-5
0.03024
0.03095
0.03235
0.03374
0.7132
0.7111
100 0.9458
120 0.8977
140 0.8542
2.264 x 10-5
2.522 x 10-5
1011
1013
0.7073
2.345 x 10-5
2.745 x 10-5
0.7041
1016
2.420 x 10-5
2.975 x 10-5
0.03511
0.03646
0.7014
1019
2.504 x 10-5
3.212 x 10-5
0.6992
160 0.8148
180 0.7788
200 0.7459
250 0.6746
300 0.6158
0.03779
3.455 x 10-5
0.6974
1023
1033
0.04104
0.04418
1044
4.091 x 10-5
4.765 x 10-5
0.6946
0.6935
350 0.5664
2.577 x 10-5
2.760 x 10-5
2.934 x 10-5
3.101 x 10-5
3.261 x 10-5
3.415 x 10-5
1056
0.04721
5.475 x 10-5
400 0.5243
1069
0.6937
0.6948
0.05015
6.219 x 10-5
0.4880
1081
0.05298
450
500 0.4565
6.997 x 10-5
0.6965
1093
0.05572
3.563 x 10-5
7.806 x 10-5
0.6986
600 0.4042
1115
0.06093
3.846 x 10-5
9.515 x 10-5
0.7037
700 0.3627
1135
0.06581
4.111 x 10-5
1.133 x 10-4
0.7092
800 0.3289
1153
0.07037
4.362 x 10-5
1.326 x 10-4
0.7149
0.3008
1169
4.600 x 10-5
1.529 x 10-4
900
1000 0.2772
0.07465
0.07868
0.7206
1184
4.826 x 10-5
1.741 x 10-4
0.7260
1500 0.1990
1234
5.817 x 10-5
2.922 x 10-4
0.09599
0.11113
0.7478
2000 0.1553
1264
5.664 x 10-4
6.630 x 10-5
4.270 x 10-4
0.7539
pressure P (in atm) other than 1 atm are
Note: For ideal gases, the properties C, K., and Pr are independent of pressure. The properties p, v, and a at a
determined by multiplying the values of p at the given temperature by P and by dividing vand a by P.
Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Original sources: Keenan, Chao, Keyes, Gas Tables, Wiley, 198;
and Thermophysical Properties of Matter, Vol. 3: Thermal Conductivity, Y. S. Touloukian, P. E. Liley, S. C. Saxena, Vol. 11: Viscosity, Y. S. Touloukian,
S.C. Saxena, and P. Hestermans, IFI/Plenun, NY, 1970, ISBN 0-306067020-8.
Transcribed Image Text:TABLE A-15 Properties of air at 1 atm pressure Dynamic Kinematic Prandtl Temp., Density, Specific Heat, Cp. J/kg. °C Thermal Conductivity, k, W/m. °C Thermal Diffusivity, a, m²/s Viscosity, Number, T, °C p. kg/m³ Viscosity, v, m²/s μ, kg/m-s Pr -150 2.866 983 -100 2.038 3.013 x 10-6 5.837 x 10-6 966 0.01171 0.01582 0.01979 0.02057 0.7246 0.7263 0.7440 -50 1.582 -40 1.514 999 9.319 x 10-6 1002 1.008 x 10-5 0.7436 1004 0.02134 -30 1.451 -20 1.394 -10 8.636 x 10-6 1.189 x 10-6 1.474 x 10-5 1.527 x 10-5 1.579 x 10-5 1.630 x 10-5 1.680 x 10-5 1.729 x 10-5 1.754 x 10-5 1.778 x 10-5 1005 0.02211 1.341 1006 0.02288 1.087 x 10-5 1.169 x 10-5 1.252 x 10-5 1.338 x 10-5 1.382 x 10-5 0.7425 0.7408 0.7387 0.7362 1006 0.02364 1006 0.02401 1006 0.02439 1.426 x 10-5 1.470 x 10-5 0.02476 0 1.292 5 1.269 10 1.246 15 1.225 20 1.204 25 1.184 30 1.164 35 1.145 40 1.127 1.802 x 10-5 0.7350 0.7336 0.7323 0.7309 1007 1007 0.02514 1.516 x 10-5 1.825 x 10-5 1.849 x 10-5 1.562 x 10-5 0.02551 0.02588 1.872 x 10-5 1007 1007 1007 1007 0.7296 0.7282 0.7268 0.7255 0.02625 0.02662 0.02699 1.608 x 10-5 1.655 x 10-5 1.702 x 10-5 1.750 x 10-5 1.895 x 10-5 1.918 x 10-5 1.941 x 10-5 45 1.109 1007 50 1.092 1007 0.02735 1.963 x 10-5 1.798 x 10-5 1.896 x 10-5 1.059 1007 60 70 1.028 0.02808 0.7241 0.7228 0.7202 0.7177 2.008 x 10-5 2.052 x 10-5 1007 0.02881 1.995 x 10-5 4.158 x 10-6 8.036 x 10-6 1.252 x 10-5 1.356 x 10-5 1.465 x 10-5 1.578 x 10-5 1.696 x 10-5 1.818 x 10-5 1.880 x 10-5 1.944 x 10-5 2.009 x 10-5 2.074 x 10-5 2.141 x 10-5 2.208 x 10-5 2.277 x 10-5 2.346 x 10-5 2.416 x 10-5 2.487 x 10-5 2.632 x 10-5 2.780 x 10-5 2.931 x 10-5 3.086 x 10-5 3.243 x 10-5 3.565 x 10-5 3.898 x 10-5 4.241 x 10-5 4.593 x 10-5 4.954 x 10-5 5.890 x 10-5 6.871 x 10-5 7.892 x 10-5 8.951 x 10-5 1.004 x 10-4 1.117 x 10-4 1.352 x 10-4 1.598 x 10-4 1.855 x 10-4 2.122 x 10-4 2.398 x 10-4 3.908 x 10-4 80 0.9994 1008 0.02953 2.096 x 10-5 2.097 x 10-5 0.7154 90 0.9718 1008 2.139 x 10-5 2.201 x 10-5 1009 2.181 x 10-5 2.306 x 10-5 0.03024 0.03095 0.03235 0.03374 0.7132 0.7111 100 0.9458 120 0.8977 140 0.8542 2.264 x 10-5 2.522 x 10-5 1011 1013 0.7073 2.345 x 10-5 2.745 x 10-5 0.7041 1016 2.420 x 10-5 2.975 x 10-5 0.03511 0.03646 0.7014 1019 2.504 x 10-5 3.212 x 10-5 0.6992 160 0.8148 180 0.7788 200 0.7459 250 0.6746 300 0.6158 0.03779 3.455 x 10-5 0.6974 1023 1033 0.04104 0.04418 1044 4.091 x 10-5 4.765 x 10-5 0.6946 0.6935 350 0.5664 2.577 x 10-5 2.760 x 10-5 2.934 x 10-5 3.101 x 10-5 3.261 x 10-5 3.415 x 10-5 1056 0.04721 5.475 x 10-5 400 0.5243 1069 0.6937 0.6948 0.05015 6.219 x 10-5 0.4880 1081 0.05298 450 500 0.4565 6.997 x 10-5 0.6965 1093 0.05572 3.563 x 10-5 7.806 x 10-5 0.6986 600 0.4042 1115 0.06093 3.846 x 10-5 9.515 x 10-5 0.7037 700 0.3627 1135 0.06581 4.111 x 10-5 1.133 x 10-4 0.7092 800 0.3289 1153 0.07037 4.362 x 10-5 1.326 x 10-4 0.7149 0.3008 1169 4.600 x 10-5 1.529 x 10-4 900 1000 0.2772 0.07465 0.07868 0.7206 1184 4.826 x 10-5 1.741 x 10-4 0.7260 1500 0.1990 1234 5.817 x 10-5 2.922 x 10-4 0.09599 0.11113 0.7478 2000 0.1553 1264 5.664 x 10-4 6.630 x 10-5 4.270 x 10-4 0.7539 pressure P (in atm) other than 1 atm are Note: For ideal gases, the properties C, K., and Pr are independent of pressure. The properties p, v, and a at a determined by multiplying the values of p at the given temperature by P and by dividing vand a by P. Source: Data generated from the EES software developed by S. A. Klein and F. L. Alvarado. Original sources: Keenan, Chao, Keyes, Gas Tables, Wiley, 198; and Thermophysical Properties of Matter, Vol. 3: Thermal Conductivity, Y. S. Touloukian, P. E. Liley, S. C. Saxena, Vol. 11: Viscosity, Y. S. Touloukian, S.C. Saxena, and P. Hestermans, IFI/Plenun, NY, 1970, ISBN 0-306067020-8.
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